When the demand for a product falls, why do costs of production go down in an increasing cost industry?

When the demand falls, surplus resources will be available in this industry. The input markets for this increasing cost industry will not clear at their existing prices, and they will have to fall. Suppliers of raw materials would prefer to sell at lower prices than to not sell at all. Similarly, we would expect workers to prefer lower wages to unemployment. For these reasons, the long-run supply curve is upward sloping, whether firms are experiencing an increase or a decrease in demand.